Introduction

The relatively new field of quantum computing has seen rapid growth in
the past two decades. Quantum computing spans the theoretical and
applied sides of both computer science and quantum physics. From its
beginnings as a thought experiment, its growth into formal system, and
finally its detailed analysis and construction, the development of
quantum computing has paralleled the early development of classical
computing.

In Section 1.1 we briefly examine some of the reasons for
interest in quantum computing. We then turn our attention to early
results and prominent quantum algorithms in Section 1.2.
We review the theory and notation of quantum computing in Section
1.3. Following that we underline the importance of lower
bounds in Section 1.4, and summarize our results in
Section 1.5.